A unified description of ordering in HCP Mg-RE alloys
High throughput first-principles calculations were employed to unravel the thermodynamic stability of two sets of hierarchical phases, β P ''' and β S ''' , in Mg-RE (rare-earth) alloys. The β P ''' orderings (with compositions greater than x RE =0.125) are predicted to form in the Mg-{La,Ce,Pr,Nd,Pm,Sm} binary alloys, thus explaining experimental observations of RE atoms arranged as hexagonal rings in these alloys. Mg-{Sc,Y,Tb,Dy,Ho,Er,Tm,Lu} alloys are predicted to form β S ' (x RE =0.125) precipitates without hexagonal ring arrangements. The calculated misfit strains are used to infer the qualitative shapes of the precipitates and their relative aspect ratios. High aspect-ratio precipitates may be formed using alloying elements that encourage the formation of β P ''' . The predictions in this study can be used to inform alloy design of precipitation strengthened magnesium alloys.